Bài 5. a) So sánh hai phân số A = 2023/2024 + 2024/2025 + 2025/2026
B = (2023 + 2024 + 2025)/(2024 + 2025 + 2026)
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1 tạ 28kg=128kg
1 yến=10kg
Khối lượng măng khô bác Hưng thu về là:
128:16x10=8x10=80(kg)
thể tích của hình chữ nhật là : 5 x 2 x 1,5 = 15 ( cm3 )
đáp số:15 cm3
g: \(\left(-\dfrac{7}{9}+\dfrac{3}{17}\right)+\dfrac{-2}{9}\)
\(=-\dfrac{7}{9}-\dfrac{2}{9}+\dfrac{3}{17}=-1+\dfrac{3}{17}=-\dfrac{14}{17}\)
h: \(-\dfrac{5}{8}-\left(\dfrac{9}{6}+\dfrac{-9}{8}\right)\)
\(=-\dfrac{5}{8}-\dfrac{3}{2}+\dfrac{9}{8}\)
\(=\dfrac{4}{8}-\dfrac{3}{2}=\dfrac{1}{2}-\dfrac{3}{2}=-\dfrac{2}{2}=-1\)
i: \(-\dfrac{2}{9}\cdot\dfrac{12}{8}+\dfrac{-3}{8}\cdot\dfrac{-2}{9}\)
\(=\dfrac{-2}{9}\left(\dfrac{12}{8}-\dfrac{3}{8}\right)\)
\(=-\dfrac{2}{9}\cdot\dfrac{9}{8}=-\dfrac{2}{8}=-\dfrac{1}{4}\)
g) $(-\frac79+\frac{3}{17})+\frac{-2}{9}$
$=(-\frac79+\frac{-2}{9})+\frac{3}{17}$
$=-1+\frac{3}{17}$
$=-\frac{17}{17}+\frac{3}{17}=-\frac{14}{17}$
h) $-\frac58-(\frac96+\frac{-9}{8})$
$=-\frac58 -\frac96+\frac98$
$=(-\frac58+\frac98)-\frac96$
$=\frac{4}{8}-\frac{3}{2}$
$=\frac12-\frac32=-\frac22=-1$
i) $-\frac29 \cdot \frac{12}{8}+\frac{-3}{8}\cdot \frac{-2}{9}$
$=-\frac13+\frac{1}{12}$
$=-\frac{4}{12}+\frac{1}{12}=-\frac{3}{12}=-\frac14
15: \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{2021}{2022}\)
=>\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2021}{2022}\)
=>\(1-\dfrac{1}{x+1}=\dfrac{2021}{2022}\)
=>\(\dfrac{1}{x+1}=\dfrac{1}{2022}\)
=>x+1=2022
=>x=2021
14: \(3^{x+1}+3^{x+1}\cdot4=45\)
=>\(3^x\cdot3+3^x\cdot12=45\)
=>\(3^x=3\)
=>x=1
11: \(\dfrac{13}{15}-\left(\dfrac{13}{21}+x\right)\cdot\dfrac{7}{12}=\dfrac{7}{10}\)
=>\(\dfrac{7}{12}\left(x+\dfrac{13}{21}\right)=\dfrac{13}{15}-\dfrac{7}{10}=\dfrac{1}{6}\)
=>\(x+\dfrac{13}{21}=\dfrac{1}{6}:\dfrac{7}{12}=\dfrac{1}{6}\cdot\dfrac{12}{7}=\dfrac{2}{7}\)
=>\(x=\dfrac{2}{7}-\dfrac{13}{21}=-\dfrac{7}{21}=-\dfrac{1}{3}\)
12: \(720:\left[41-\left(2x-5\right)\right]=2^2\cdot5\)
=>\(41-\left(2x-5\right)=\dfrac{720}{20}=36\)
=>2x-5=5
=>2x=10
=>x=5
9: \(\dfrac{4}{x}=\dfrac{y}{21}=\dfrac{28}{49}\)
=>\(\dfrac{4}{x}=\dfrac{y}{21}=\dfrac{4}{7}\)
=>\(\left\{{}\begin{matrix}x=7\\y=21\cdot\dfrac{4}{7}=12\end{matrix}\right.\)
\(\left(\dfrac{31}{42}\times\dfrac{17}{25}+\dfrac{31}{42}\right)\times\left(-5\right)^2\)
\(=\dfrac{31}{42}\times\left(\dfrac{17}{25}+1\right)\times25\)
\(=\dfrac{31}{42}\times\dfrac{42}{25}\times25=31\)